where [tex]$y = \sqrt \alpha x$
[/tex]
First of all, does this mean replace all alphas, and x's with y's? (Is it even possible to get rid of all x's? I end up with a y/x in there), and then apply
d(chi)/dy-y*chi
Is that what the operator is doing? I don't see the significane of the answer. If I apply the lowering operator (d/dy + y) I still get 'an' answer, when I figure I should get something to tell me I can't go lower then the groud state (a zero perhaps, or a mathematical impossibility like division by zero)

Anyway...if anyone can shed some light on this it would eb much appreciated!

Edit: I cant figure out division on this board! I swear to god I am doing it right...I will post my operator down here...if someone can point out the latex error I'd love to know:
[tex]\[
\frac{d}
{{dy}} - y
\]